Enhancing pension adequacy while reducing the fiscal budget and creating essential capital for domestic investments and growth: Analysing the risks and outcomes in the case of Greece

Symeonidis, Georgios; Tēnios, Platōn; Xenos, Panos Article Enhancing pension adequacy while reducing the fiscal budget and creating essential capital for domestic investments and growth: Analysing the risks and outcomes in the case of Greece Risks Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Symeonidis, Georgios; Tēnios, Platōn; Xenos, Panos (2021) : Enhancing pension adequacy while reducing the fiscal budget and creating essential capital for domestic investments and growth: Analysing the risks and outcomes in the case of Greece, Risks, ISSN 2227-9091, MDPI, Basel, Vol. 9, Iss. 1, pp. 1-17, https://doi.org/10.3390/risks9010008 This Version is available at: https://hdl.handle.net/10419/258098 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ risks Article Enhancing Pension Adequacy While Reducing the Fiscal Budget and Creating Essential Capital for Domestic Investments and Growth: Analysing the Risks and Outcomes in the Case of Greece Georgios Symeonidis * , Platon Tinios and Panos Xenos   Citation: Symeonidis, Georgios, Platon Tinios, and Panos Xenos. 2021. Enhancing Pension Adequacy While Reducing the Fiscal Budget and Creating Essential Capital for Domestic Investments and Growth: Analysing the Risks and Outcomes in the Case of Greece. Risks 9: 8. https://doi.org/10.3390/risks9010008 Received: 4 November 2020 Accepted: 23 December 2020 Published: 29 December 2020 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Department of Statistics and Insurance Science, School of Finance and Statistics, University of Piraeus, Karaoli ke Dimitriou 80, 18534 Piraeus, Greece; [email protected] (P.T.); [email protected] (P.X.) *Correspondence: geor[email protected] Abstract: Many countries around the world are resorting to mandatory funded components in their multi-pillar pension systems with the purpose of catering for the financial pressure from ageing. This paper aims at analysing the possible replacement rates for such a scheme, by choosing different assumptions and setting the best combined area for the expected result. Then, an approach for analysing the potential for the implementation of such a scheme in Greece is presented along with the actuarially projected expected benefit expenditure and respective accrued capital. A result of the introduction of such a component is expected to be the elevated replacement rate at retirement with a concurrent alleviation of the fiscal burden for the state. The projected scale of savings will also provide domestic financing for investments generating growth. Keywords: funded pensions; adequacy; capital investment; growth 1. Introduction This paper aims to estimate the effect on replacement of the potential introduction of a mandatory fully funded scheme in the Greek pension system. This goal will be achieved by analysing three parameters and providing an approach to determining the optimal mix of the three. The proposed approach is based on a three-dimensional analytical tool that brings together the essential parameters: (1) The average number of years of the annuity (e.g., life 2 expectancy at the age of claiming the annuity), (2) the expected return on investments, and (3) the contribution rate applied to the pensionable earnings of the nation’s participants. An actuarial projection of the benefits and contributions (assets) using the cohort method for the total of employed people in Greece is also conducted to provide an analysis of the projected effects of a possible implementation of this system on the accrued capital, the government budget and over national debt. The Greek pension system is likely to suffer a great deal in the future due to the population ageing, with a 16% decline in population from 2019 to 2060, while at the same time, it has been underfunded in the past decades (EPC 2015b,2015c,2018). The state is also expected to be one of the four European states to surpass 65% old-age dependency ratio in 2070 (EPC 2020). Moreover, since Greece’s population is dramatically shrinking, this is expected to put great pressure on the country, with a quickly rising demographic dependency ratio, compared to the European average (EPC 2018). The sustainability of the system has long been in question. Recent pension reforms have proved unsuccessful in restoring the financial stability of the pension system (EPC 2015b,Symeonidis 2016). The pension expenditure in Greece has exceeded 17.5%, of Gross domestic product (GDP) in 2016 (Eurostat 2019) with the European average at 11.2% of GDP, while contribution rates vary from 27 to over 30% for the pension branch, being one of the highest rates in the EU (EPC 2018). Such a burden to the economy nurtures uncertainty for pensioners and Risks 2021,9, 8. https://doi.org/10.3390/risks9010008 https://www.mdpi.com/journal/risks Risks 2021,9, 8 2 of 17 undermines competitiveness. Except for the continuous legislation changes, horizontal pension cuts have deprived some pensioners of more than 50% of their income. Losses were heaviest among those contributing most, which is inversely proportional to reciprocity 1 . The reforms and cuts were all a result of the necessity of external funding of the Greek economy by the European Commission, the European Central Bank and the International Monetary Fund after the Greek prime minister turned to these for help in 2010, under extreme financial conditions and near bankruptcy. In 2017 and 2018 there seems to be a slight increase in contribution collection brought by the latest legislation, but nevertheless the funding gap of the system remains close to 50% (Government Official Journal 2018). In this respect, providing financial stability while securing adequate pensions and acceptable level of consumption in retirement incomes remains a very difficult task to achieve, especially when (Pay-As-You-Go) PAYG systems are coupled with intense population ageing. PAYG has the dominant role in the Greek pension system, while occupational schemes and private insurance are practically non-existent. More explicitly, PAYG (social security benefits) payments for primary and secondary pensions in 2017 and 2018 amounts to 24 billion EUR per year (Government Official Journal 2018), while occupational pension funds pay almost 90 million EUR (OECD.stat 2020) and private insurance companies almost 28 million EUR (Hellenic Association of Insurance Companies 2020). Looking into the developed countries as a whole, foreseen intense population ageing poses a financial burden in public pension systems in the present or near future. (European Commission 2010,2012;OECD 2015,2017). Most European countries that have mature payas-you-go (PAYG) defined benefit schemes are facing problems in financing these programs due to program maturation, population ageing, prior promises of overly generous benefits, changes in employment patterns or a combination of the above. The most common practice for these countries were parametric reforms or systemic reforms, which helped public pension systems deal with the increased financing needs (EPC 2015c,2018). The rest of the paper is arranged in five sections as follows. The second section provides a brief literature review on the introduction of funded schemes internationally and the relativity of the latter to the promotion of savings and potential growth. In the following section, we present the methodology and all necessary equations together with the corresponding parameters are discussed. We then present and explain the results in the fourth section. In the final section, we make discussion on and the aforementioned results. Further analysis is provided in the same section addressing the use of these findings in the implementation of funded schemes, and the Greek case is specifically stressed. 2. Literature Review Some countries decided to introduce mandatory fully funded pension schemes, as a second tier to the PAYG tier. Recent developments have led law-makers to acknowledge that fully funded components can be an integral part of an adequate third-age income. In this direction, several countries, including Sweden and some Eastern Member States such as Bulgaria, Estonia, Croatia, Latvia, Lithuania, Hungary, Poland, and Slovakia, have switched part of their public pension schemes into (quasi-) mandatory private funded schemes (EPC 2018). The introduction of funded pillars gained momentum across Europe after the 1990’s (Feldstein 1995,1996,1998). However, the reversals which followed the 2008 economic and financial crisis actually reduced or completely eliminated the role of funding in many countries (Bielawska et al. 2017). One of the main arguments in favour of funded schemes is that they promote growth. Davis and Hu (2008) argue that funding of pensions connects to higher economic growth, especially for emerging market economies, due to higher saving rates, capital market development and reduced labor market distortions. The OECD (2013) likewise stresses the importance of private pensions to economic growth, looking into the institutional role 1 Horizontal pensions cuts refer to the reduction in pension amounts based on the sole criterion of the amount itself. For example, a 20% reduction of all pensions above 1200 euros. Risks 2021,9, 8 3 of 17 of private funds, while the latter continue to grow and invest. (Bijlsma et al. 2014) link growing pension savings to general economic growth, through the investment of fund assets. Zandberg and Spierdijk (2013) conclude that the long-run effect on growth borne out of funded pensions is positive when using estimates from a model with overlapping observations, but the effect is not the same when a simple cross-sectional model is used. However, both Davis and Hu as well as Zandberg and Spierdijk (2013) have been challenged by (Cavallini et al. 2013). The latter proceeded to re-estimate the Davis and Hu (2008) by using the total pension fund assets definition of Zandberg and Spierdijk (2013) and a more sophisticated common correlated effects mean group (CCEMG) and common correlated effects pooled (CCEP) estimators (accounting for a multifactor error structure) for 12 OECD countries over the period 2001–2010. (Cavallini et al. 2013) have ultimately found no evidence of a long-term relationship between pension fund assets and economic growth. Overall, the preliminary data for 2019 show that pension funds held USD 32.3 trillion in the OECD area (OECD 2020) while the nominal investment rates of return of all funded and private pension plans vary between 2.3% and 9.7% for the years 2015–2019 (OECD 2019a). Having said that, let there be no doubt that funded schemes, as PAYG schemes, also come with flaws. After all, the main question that Lindbeck and Persson (2003) asked before reforming the Swedish pension system, whether there is an ideal system, remains rhetorical in essence. On the one hand, according to Barr (2000) it would be possible to achieve essentially the same result by making similar benefit cuts and tax increases in the existing PAYGO DB schemes, but this has not proved to be very successful, maybe because of the political implications it involves, rather than introducing a new pension type. On the other hand, in the funded schemes, fluctuations in stock and bond markets are the principal risk experienced by investors; this is why a funded component must always be part of a cohesive savings strategy including the other, ostensibly safer, pillars and components. More specifically, Góra and Palmer (2020) conclude that, although funded schemes are expected to generate a higher rate of return than notional funded schemes, they are considerably more volatile, which makes them appropriate for a second pillar but not a first universal (mandatory) public pillar. As regards the differences in efficiency between fully funded and notional schemes, Góra and Palmer (2004) further compare the efficiency of the fully funded schemes as opposed to other types of schemes concluding amongst other that the fully funded schemes are potentially superior to notional schemes because they can create saving and promote financial market development. Finally, Holzmann and Hinz (2005) argue that successful reform of pensions depends first and foremost on a careful consideration of the macroeconomic and fiscal environment and whether the latter can support the reform. 3. Methodology 3.1. Funded Schemes—Formulas and Parameters Let us analyse the three parameters mentioned above (annuity, return on investment, contribution rate) and build on the logic of our calculations. The idea behind funded systems is that each contributor sets aside a certain amount of money per period of time; in the end of their working life, they get back the accumulated funds. These correspond to the future present value of the amounts paid, increased by the return on investment, and paid out in the form of a lifelong pension flow (annuity). Hence, a simplified formula describing the accrued amount would be: Acc =∑n i=1X(1+i)n(1) where: Acc: is the accrued amount at retirement, X: is the amount of contributions per year (assumed fixed), i: is the yearly rate of return on investment, Risks 2021,9, 8 4 of 17 n: is the number of years of contribution 3.1.1. The Baseline Scenario Analysis Let us assume that a new mandatory, fully funded system starts today, without any financial burden from past commitments. The potential transition from an already existing system and its financial burden is not analyzed in this paper and could be a topic for further analysis. A critical indicator in such a system is the projected replacement rate at the time of retirement. The replacement rate is defined as the fraction of the first pension amount, over the last wage. Sometimes, yet not in this paper, the denominator is also computed as the average career income instead of the last wage, which introduces an element of confusion. In order to calculate representative replacement rates for the fully funded system, we first have to further specify formula (1). Starting from formula (1) and looking into a more complex case, we can account for income variability and maturity, in order to calculate the required contribution rate as a percentage of a specific amount of income (e.g., 6% on earnings). In addition, we can take into account a percentage of expenses on contributions. In this context, the accrued amount at time n shall be given by: Accn=Xn∗(1−E)(1+i)1 2+Accn−1(1+i)(2) where: Accn: is the accrued amount at time n, Xn: is the amount of contributions at time n as percentage of income, before expenses, E: is the percentage of expenses on contributions, i: is the yearly rate of return on investment, n: is the number of years of contributions The annual return rate on investment (i) is assumed to be constant for the purpose of simplicity. Payments are assumed monthly; hence, the amount of the last year is multiplied by (1+i)1 2as if there were one payment in the middle of the year, to simplify. Let us use formula (2) and proceed to calculate the replacement rate for a proposed funded scheme. To do that, certain additional assumptions are needed. These are the salary maturity per year 2 , a possible contribution rate which would serve as a norm or as the minimum3, an expense rate on contributions and a real return rate (after expenses). An annuity is needed to convert the funds accumulated into a pension at retirement. In most of the developed countries but also elsewhere, recent legislation and reform trends indicate a full working career of about 40 years for a full pension and the retirement age thresholds are typically at an age between 62 and 67 years. In this paper, the full career is assumed to be close to the maximum, hence 40 years. We shall also assume an average/representative annuity of 15.64, which is a joint annuity based on EVK2000 4 and HAS 5 2005 tables. This annuity corresponds to the Greek mandated (67) age threshold which is slightly higher than the effective retirement age in most cases. However, given extensive reforms over the bailout period, forward-looking assumptions may reasonably differ from historical data. Since, however, the mortality tables come in many variations according to country, e.g., continent, race, employment, and so on, so other values for the annuity are also assumed in the sensitivity analysis. 2The percentage of increase of a person’s salary due to legislated increase based on more years of work, an increase in pay or a promotion. 3 Legislators are expected to present people with a standard percentage of contribution to either begin with or serve as the standard where choice is not made. 4 EVK2000 is the official mortality table for valuations reported to the Secretariat-General for Social Insurance, based on Gazette B1432/2006, Ministerial Decision 2. Mortality of Greeks is greater than that of the Swiss, a fact which provides better benefits when the EVK2000 is used for the Greek population. 5Hellenic Actuarial Society. Risks 2021,9, 8 5 of 17 Since we are looking into a scheme that is mandatory, a minimum contribution rate on pensionable earnings is assumed for organizational reasons. This will be set at 6% of pensionable earnings to begin with, based on European experience (European Commission 2008). Further analysis on other possible contribution rates is provided in the sensitivity scenarios. Other assumptions include 0.5% maturity per year on income and an expense rate of 0.5% on contributions. The real return rate (RRR) is our final and maybe the most important variable and should be thoroughly investigated before selecting a working assumption for our baseline. Firstly, there is a case to be made about current returns being very low because of quantitative easing 6 in an attempt to reduce the effects of the recent monetary crisis that started in 2008 (Rajan 2019) and more recently with the depression that started in February 2020 due to the COVID-19 pandemic. In his comparative report, covering almost 200 pension funds, with more than 3 trillion assets under management/advisement, in 50% of pension plan respondents, quantitative easing was reported to have undermined the longer-term financial viability of pension plans. At the same time, 62% of respondents reported that quantitative easing has overinflated the value of pension liabilities via zero-bound interest rates. It is also mentioned that falling rates also inflate the present value of future liabilities, as measured under prevailing pension regulation. As a ball park estimate, the report mentions, a 1% fall in rates delivers a 20% rise in pension liabilities and a 10% fall in the funding ratio—a measure of a plan’s ability to meet its future commitments. As with very low or zero interest rates, negative interest rate policy also creates problems as regards pension returns as these exacerbate effects of low (but positive) policy rates and quantitative easing (IMF 2017). Expanding the view to a longer period, as regards future returns, Gratton and Scott (2018) argue that it is important to use longer historical data periods for forecasts, as many as 100 years or even more. Based on data from Credit Suisse, they calculated return rates for many large countries for the years 1900 to 2014 and concluded that the long-term returns for zero-risk investments was close to 2% for the US, but 6.4% for risk premiums. Consequently, for a mixed portfolio of 50% zero risk bonds and 50% stocks, one would earn 4.2% on average in the long term. For the UK, the respective return is 3.5%. The average historical returns for the US, the UK, Japan, Germany, France, and Australia are 2.8% above inflation. In the OECD (2015,2017,2019b), the real rate of return on funded, defined contribution pensions for calculations is assumed to be 3% per year. In the Pension Adequacy Report (European Commission 2018), the assumed rate for the base case is 3% while the interest rate assumed to calculate the annuity is 0.8% lower than the assumed rate used during the accumulation phase, in order to account for the cost of buying the annuity, administrative and management expenses. Based on the analysis of the averages of the 20-year through 30-year maturity of the Zero-coupon yield curve spot rates of AAA-rated euro area central government bonds and the whole euro area central governments bonds (Eurostat 2018), we see in the table below that the averages vary between 2.12% to 2.76%. This gives values, which have to be assumed as minima, as the whole period of the crisis is included. Table 1contains zero-coupon yield curve spot rates for all Euro Area (EA) bonds as well as all AAA bonds, for different time intervals and years of maturity. 6 Quantitative easing (QE) is a form of unconventional monetary policy in which a central bank purchases longer-term securities from the open market in order to increase the money supply and encourage lending and investment. Buying these securities adds new money to the economy, and also serves to lower interest rates by bidding up fixed-income securities. It also expands the central bank’s balance sheet. Source: https: //www.investopedia.com/. Risks 2021,9, 8 6 of 17 Table 1. Zero-coupon yield curve spot rates. Maturity/Time All EA Average 10 (2008–2017) AAA Average 10 (2008–2017) All EA Average 10 (2004–2013) AAA Average 10 (2004–2013) Maturity: 10 years 2.82 2.12 3.86 3.38 Maturity: 20 years 3.50 2.73 4.38 3.88 Maturity: 25 years 3.61 2.77 4.46 3.91 Maturity: 30 years 3.65 2.76 4.48 3.90 Source: (Eurostat 2018), calculations by authors. If we look back at earlier years, the respective values are much higher, reaching 5% for the years 2004–2013. If we looked back at the data even before the crisis started, the rates would rise even more. For example, the respective spot rate for 20-year maturity of EA bonds was 5.5% in 1999 (Eurostat 2012). The deep correction during the Greek crisis could imply, as happened in the cases of Spain, Cyprus and Portugal, some re-alignment concerning returns especially in the first post crisis years. In conclusion, the baseline case, a 3.5% return is a prudent assumption for a time period close to the full working career. The authors do take into account that there is intense discussion ( Lukaszl and Summers 2019 ; Schmelzing 2020) about the long-term decline on returns and treat this issue with sensitivity analysis in Section 3.1.2.2, where a minimum return of 2% is chosen. Blending the two aforementioned inquiries, we choose RRR in our basic scenario to be 3.5%. Using the assumptions mentioned before and outlined in Table 2, we estimate that the replacement rate is calculated at 26.02% for 40 years or 0.65% yearly, for an annuity of 15.64 years. These can be found in Table 2. Table 2. Assumptions on calculating the replacement rates for the defined contribution fund ETEA. Income maturity 0.50% Total contribution rate 6.00% Expenses on contributions 0.50% Total working life in years 40 Expected life of the annuity 15.64 Source: calculations by authors. We observe that the replacement rate covers a significant amount of return on retirement, with a contribution of 6% on pensionable income. To benchmark this for the Greek case (follows in the paradigm section), let us say that for the same amount of contributions, the present system replaces at 0.45% yearly. More specifically, the latest pension reform of 2016 replaces contributions at 0.45% yearly for the years until 2014, while for 2015 and on the system works on NDC principles and takes into account the annual wage growth. Let us look at the further options for replacement below, while expanding the main calculation variables chosen in the baseline. 3.1.2. Sensitivity Analysis In the previous subsection, a careful selection of assumptions was made. However, sensitivity analysis is deemed necessary so that possible extreme behaviour of the system is highlighted while still in the planning period. 3.1.2.1. Annuity Sensitivity One of the assumptions to analyse further would be the annuity and the expected life span it refers to. Life expectancy not only varies greatly from country to country, but is also increasing. Moreover, the choice of whether or not to transfer the annuity to a spouse, if the contributor dies, implied a range of values to look into in order to determine the possible outcomes for the respective replacement rates. The normal retirement age for men and women around Europe varies between 62 and 67 years old, while some countries (EPC 2018) tend to reform in the direction of a Risks 2021,9, 8 7 of 17 part of the future increase in life expectancy be incorporated in the statutory retirement age. The fully funded private pension schemes are not usually subject to a minimum retirement age, as the choice of leaving the work force is based on the amount amassed at that point, since ownership is one of the most important aspects of such funds. However, since this paper is looking into a mandatory funded scheme, which in the Greek case will go hand-in-hand with the social security pension, it is prudent that people be asked to fulfil the criteria for a primary pension before retiring from the funded scheme. Having chosen an annuity based on the EVK2000, we now enrich our research using the mortality tables GR1990 7 , PM6064 8 , and HAS 2005 and 2012 tables. Based on these, we will look for a possible annuity range to fulfil the sensitivity analysis, focusing on the most recent tables. For the PM6064 mortality table, we calculate ages at last birthday, (e.g., age 67.7 is calculated as age 67) and subtract five years for women and two years for men in order to better convey the increase in longevity and allow for the fact that these tables are dated. This method—using PM6064 and subtracting years to cater for the increase in longevity – is common/standard practice in the Greek pension calculations 9 . The results are depicted in the tables below. Table 3refers to the average length of the pay-out period with longevity based on unisex life expectancy for women as well as men for the first two columns, and to each gender for the next four. Table 3. Ages and respective annuities under different mortality tables. EAA2012 EAA2005 PM6064 GR1990 AGE Unisex Unisex Men (-2) Women (-5) Men Women 62 24.70 21.71 16.30 18.39 18.36 21.04 63 23.84 20.90 15.63 17.68 17.62 20.18 64 22.99 20.11 14.97 16.98 16.88 19.32 65 22.15 19.34 14.33 16.30 16.16 18.47 66 21.32 18.57 13.71 15.63 15.46 17.62 67 20.50 17.82 13.10 14.97 14.77 16.80 68 19.70 17.08 12.50 14.33 14.10 15.98 69 18.91 16.36 11.93 13.71 13.45 15.19 70 18.13 15.66 11.37 13.10 12.81 14.42 Source: Calculations by authors. As long as the legislated normal retirement age for the primary pension in Greece is still 67, a prudent set of values derived from the above table is from 14.00 and proceeding to value 18.00, with a 0.1 interval. The replacement rates arising from the main annuity values can be found in Table 4. Table 4. Main annuity values and respective replacement rates. Annuity 14 15 16 17 18 Replacement 29.10% 27.10% 25.40% 24.10% 22.70% Source: calculations by authors. 3.1.2.2. Return Rate Sensitivity As mentioned earlier, sensitivity analysis on rate of return values is very important. Looking back at Table 1, we may assume values for the return rate varying between 2% and 6%. This spectrum of values covers possible cases of prudent assumptions between lower returns for crises and higher returns during intense financial growth. Again, a step 7Greek Mortality Tables, 1990 data. 8French Mortality Tables, Assured Lives, 1960–1964 Experiences, Male, used in the Greek Actuarial calculations in the past. 9Ministerial Decree D K4-4381/1979. Risks 2021,9, 8 8 of 17 of 0.1% has been chosen. The main values of the return rate and respective replacement are depicted in Table 5below: Table 5. Main return rate values and respective replacement rates. Return rate 2% 3% 4% 5% 6% Replacement 18.80% 22.80% 28.50% 36.80% 46.90% Source: calculations by authors. 3.1.2.3. Contribution Rate Sensitivity The initial/minimum contribution rate as proposed for this funded scheme is 6% on pensionable earnings. Since, however, this scheme is assumed to be fully funded, it is logical that higher contribution rates can be accepted so that people willing to set more money aside for their old age earn a higher replacement. European Commission (2008) presents the contribution rates to privately managed funded schemes across different European countries and these vary between 5% and 9%. Therefore, starting from the proposed minimum to be legislated, we examine the replacement rates for a step of 0.1% up to 10%. Table 6shows the main contribution rate values and respective replacement rates. Table 6. Main contribution rate values and respective replacement rates. Contribution rate 6% 7% 8% 9% 10% Replacement 26.00% 30.40% 34.70% 39.00% 43.40% Source: calculations by authors. 3.2. Methodology for the Greek Case Study The Greek case study has been utilized using the cohort simulation projection method. Several European countries use such models for their social security systems (European Commission 2007) Cohort simulation projection models are based on up-to-date crosssectional information regarding the labour activity and social security contributions by various social groups (cohorts). Further break-down by gender, position in the labour market and demographic characteristics is also possible and has been taken into consideration (TARKI 2008). The input is based on aggregate data for the cohorts instead of person-by-person specific data. The averages are projected for each year using formulas for demographics and finances. The transition from year tto year t+ 1 changes the status of a person (active, inactive or pensioner) and is mapped onto the following year using the actuarially assumed transition probabilities. These are included in the mortality tables as analysed earlier in the text, and the assumptions on retirement rates which are calculated through the experience of the historical data of the last few years before the base year of the projection. The projection of the active population from t − 1 to time t is expressed by the following equation: Act(x,s,t)=Act (x−1, s−1, t−1)·px−1(aa)(3) The interpretation of the above equation is the following: The active population at time t, aged xwith s years of past service equals the active population aged x − 1 of the previous year, with s − 1 years of service multiplied by the probability of a person aged x − 1 to stay active. An active person may become inactive through retirement, invalidity, death and unemployment. On the income side, the contribution base can be calculated as the product of the number of contributors by the average insurable earnings. On the other hand, benefit expenditure is calculated as the result of the product of benefit expenditure in year (t − 1) Risks 2021,9, 8 15 of 17 for the financial pressure from ageing and enhance post-retirement stability, supporting the financing of consumption after retirement. At the same time, it may help reduce implicit pension debt and general government in a direct and indirect way respectively, by reducing future pension deficits and boosting economy and growth, which will consequently help increase employment. Finally, amassing contributions from the new funded scheme corresponding to large percentages of GDP and investing them could lead to safer pensions and better returns. If used wisely and well organized, political alternation has minimum impact. Author Contributions: All authors have contributed substantially to this work. Conceptualization, G.S. and P.X.; Methodology, G.S.; Software, G.S.; Validation, G.S.; Formal Analysis, G.S.; Investigation, G.S.; Resources, G.S., P.T. and P.X.; Data Curation, G.S.; Writing—Original Draft Preparation, G.S.; Writing—Review & Editing, G.S., P.T. and P.X.; Visualization, G.S. Supervision, G.S., P.T. and P.X.; Project Administration, G.S., P.T. and P.X.; Funding Acquisition, P.X. All authors have read and agreed to the published version of the manuscript. Funding: The publication of this paper has been partly supported by the University of Piraeus Research Center. More specifically, the APC was funded by the University of Piraeus Research Center. Acknowledgments: The authors thank the referees for their comments which helped to improve the manuscript. The authors would also like to thank Vasiliki Takou and Alberto La Mantia for useful insight regarding the best way to present data for replacement. Conflicts of Interest: The authors declare no conflict of interest. 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